Published online by Cambridge University Press: 15 September 2005
The basic goal of this paper is to describe the dynamics of an m + 1-parameter family of piecewise conformal automorphisms of the Riemann sphere. In the ‘symmetric’ figure shown later (Figure 1), we observe the regions of attraction of periodic attractors. In fact, we prove that the only $\omega$-limit sets are periodic cycles. This shows that the conformality of the functions is stronger than the discontinuity.